Figure REF  presents \(\tilde{T}_{c0}\)  and \(\tilde{T}_c\)  versus \(\tilde{\mu }\) , as calculated for \(|\tilde{\varepsilon }_0|=50,70\) , and 110 at \(\lambda _{12}=0.005\)  and \(m_2/m_1=1\) . One can see that the mean-field critical temperature exhibits a significant increase when the chemical potential approaches the lower edge of the Q1D band and the Q1D Feshbach-like resonance develops. However, this increase can be compromised by the pair fluctuations. In particular, our results demonstrate that the fluctuation-shifted critical temperature approaches the mean-field one only when band 1 becomes deep enough, which is in agreement with the previous results [1]}. The reasons for this are as follows. First, \(Gi_1\)  decreases with increasing \(\tilde{\varepsilon }_0\) , as is seen from Eq. (REF ). Second, the ratio \(v_2/v_1\)  becomes larger and so does the ratio \({\cal K}^{(x)}_2/{\cal K}^{(x)}_1\) . The latter appears in the denominator of Eq. (REF ) so that an increase of \({\cal K}^{(x)}_2/{\cal K}^{(x)}_1\)  leads to a decrease of \(Gi\) . As a result, the pair fluctuations are eventually suppressed and \(\tilde{T}_c\)  approaches \(\tilde{T}_{c0}\) , as follows from Eq. (REF ).
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